UST921020I4

ABSTRACT

FACE IN SPACE AND THE COORDINATES OF THE VERTEX POINTS ARE THEREBY DETERMINED AND THE CONNECTION OF POINTS ARE COMPOSED. WHEN THE GIVEN VIEWS DO NOT CONSIST OF AN EQUAL NUMBER OF FEATURES OR WHEN A CONSTANT ALTITUDE LINE CROSSES AN UNEQUAL NUMBER OF FEATURES IN THE GIVEN VIEWS, THIS SIGNIFIES THAT A LINE HAS BEEN DRAWN THAT IS NOT THE EDGE VIEW OF A FLAT SURFACE. THE LATTER TYPE LINES ARE SUITABLY DELETED. AFTER THE FEATURES IN TWO GIVEN VIEWS ARE PROPERLY ASSOCIATED AND ALL THREE-DIMENSIONAL SURFACES THAT DO NOT APPEAR AS AREAS IN THE GIVEN VIEWS ARE FOUND, THERE ARE NOW FOUND THE HORIZONTAL SURFACES. TO EFFECT THE LATTER STEP, THERE ARE FOUND THE VERTEX POINTS THAT ARE NOT COMPLETELY DEFINED, A DEFINED VERTEX POINT BEING THE JUNCTION OF THREE OR MORE FLAT SURFACES, THE VERTEX POINT BEING TAKEN TO BE THE VERTEX OF A CONE IN SPACE FOR ALL THE SIDES OF THE CONE (EXCLUDING THE BASE) ARE COMPLETELY DEFINED. AN INCOMPLETELY DEFINED VERTEX POINT BELONGS TO A LINE WHICH HAS NOT BEEN FOUND TO LIE ON THE BOUNDARY OF AT LEAST TWO SURFACES. THE INCOMPLETELY DEFINED VERTEX POINTS ARE PLACED IN A LIST OF DECREASING ALTITUDE. THIS LIST IS INITIATED BY BEGINNING AT ANY VERTEX FOR A PARTICULAR ALTITUDE AND CONNECTING IT TO ANOTHER VERTEX AT THE SAME ALTITUDE BY MEANS OF AN EXISTING LINE. THE PROCESS IS CONTINUED UNTIL ALL OF THE VERTEX POINTS ARE CONNECTED AND THE LIST OF LINES SO GENERATED COMPLETES THE DEFINITION OF VERTEX POINTS AND ALSO COMPLETES THE POLYHEDRON DEFINITION FOR THE GIVEN VIEWS. AT THIS JUNCTURE, THE DESCRIPTION IS COMPLETE IN THE GEOMETRIC AND TOPOLOGICAL SENSE AND THE RENDERING OF ANY OTHER VIEW IS PROVIDED BY USE OF A CONVENTIONAL PROGRAM TO DRAW THE OTHER VIEW. IN THE PROCESS DESCRIBED HEREIN, THERE ARE ANALYZED TWO ORTHOGRAPHIC VIEWS AND THEN, WITH THE DATA GENERATED IN SUCH ANALYSIS THERE IS ENABLED THE GENERATION OF THE THIRD VIEW OF A POLYHEDRON. IN THE PROCESS THERE ARE FIRST DRAWN THE FRONT AND PROFILE VIEWS ON A DEVICE SUCH AS A CAPACITANCE TABLET WHICH IS UTILIZED IN ASSOCIATION WITH A COMPUTER CONTROLLED INTERACTIVE GRAPHICS DEVICE. THE VIEWS ARE DRAWN SUCH THAT END POINTS OF LINES ARE CLEARLY RECORDED, THE FRONT AND PROFILE VIEWS BEING TERMED GIVEN VIEWS. THERE IS NOW FORMED IN A TEMPORARY STORAGE AREA A LIST OF THE VERTEX POINTS CORRESPONDING TO THE VERTEX POINTS IN THE TWO GIVEN VIEWS. IN ADDITION, THERE IS FORMED IN A TEMPORARY STORAGE AREA, A LIST OF LINES CONNECTING THE VERTEX POINTS, I.E., A TOPOLOGICAL MAP. THE LIST OF STORED LINES IS ANALYZED TO FIND SETS OF LINES WHICH FORMED CLOSED LOOPS, THE LATTER CLOSED LOOPS DEFINING POLYGONS WHICH ARE VIEWS OF RESPECTIVE SURFACES ON THE POLYHEDRON. IN ADDITION, THERE ARE ALSO TAKEN AS POLYGON LINES, THOSE WHICH HAVE VERTICAL COMPONENTS. THESE LINES CAN BE FLAT SURFACES WHICH ARE SEEN IN EDGE VIEW IN THE GIVEN VIEWS, I.E., IN THE PROFILE OR FRONT VIEWS. AT THIS POINT THERE S NOW PRESENT IN STORAGE A DERIVED POINT LIST, LINE LIST AND A POLYGON LIST. IN THE POLYGON LIST, THE POLYGONS ARE NOW SORTED IN ORDER OF DESCREASING ALTITUDE. TO EFFECT THIS SORT, THERE ARE FOUND THE LINES OF CONSTANT ALTITUDE WHICH PASS ACROSS BOTH OF THE GIVEN VIEWS. THERE IS, THEREBY FORMED A LIST OF POLYGONS THAWT THIS CONSTANT ALTITUDE LINE CROSSES. WHEN THE NUMBER OF POLYGONS IN THE FRONT VIEW EQUALS THE NUMBER OF POLYGONS IN THE PROFILE VIEW, THE FEATURES CAN BE IMMEDIATELY MATCHED. SUCH MATCHING IS MADE FOR ALL ALTITUDES AND ONLY HORIZONTAL SURFACES ARE NOT DETECTED. IN THIS CONNECTION, A PAIR OF MATCHING POLYGONS, ONE FROM EACH VIEW CAN BE TAKEN TO BE TWO VIEWS OF A SUR-



